Higher Order Log-Concavity in Euler's Difference Table

2009/11/14 by William Y. C. Chen, Chen, William Y. C., Cindy C.Y. Gu +8
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.0911.2775

11 pages

arxiv created 2009/11/14 · openalex publication_date 2009/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let e_n^k be the entries in the classical Euler's difference table. We consider the array d_n^k=e_n^k/k! for 0≤ k ≤ n, where d_n^k can be interpreted as the number of k-fixed-points-permutations of [n]. We show that the sequence \d_n^k\_{0≤ k≤ n} is 2-log-concave and reverse ultra log-concave for any given n.

Citations

• Fix-Euler-Mahonian statistics on wreath products

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